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### ACS

 Reducing Basis Mismatch in Harmonic Signal Recovery via Alternating Convex SearchJonathan M. Nichols(*), Albert K. Oh(**), Rebecca M. Willett(**)IEEE Signal Processing Letters, Aug. 2014(in press)[link] [pdf] [arXiv]Download Matlab code here! (Last updated June 27, 2014)Abstract:The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact signal model can result in dramatic increases in estimation error; this is the so-called "basis mismatch" problem. This work provides one possible solution to this problem in the form of an iterative, biconvex search algorithm. The approach uses standard $\ell_1$-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art.(*) Optical Sciences Division, U.S. Naval Research Laboratory; Washington, D.C. 20375(**) Dept. of Electrical and Computer Engineering, University of Wisconsin-Madison; Madison, WI 53706